You can now get the alternative web browser Firefox for iPhone and iPad in the App Store. Except its not really Firefox as you know it on the desktop, because the underlying engine is all WebKit, not Mozilla’s Gecko renderer like it is on the Mac. This is the same as the iOS Google Chrome app — the App Store rules require browsers to use the Safari WebKit engine. This isn’t really a bad thing, the WebKit rendering core is the industry leading mobile (and desktop) engine.
You might want to use Firefox for iPhone and iPad if you use Firefox on the Mac, due to UI similarities for the browser chrome or just for syncing convenience. The Firefox app will sync bookmarks, open tabs across all your devices by logging into your Firefox account. These are the main differences between Firefox and the native Safari app.